Summary
FlowSGS is a flow-based posterior sampling method for solving inverse problems in computational imaging, proposed by Tianao Li, Xinhui Qian, and Emma Alexander (arXiv:2609.20769). Existing flow-based inverse solvers assume linear forward models and/or rely on simplifying approximations in posterior sampling. FlowSGS addresses this by using Split Gibbs Sampling (SGS) to decompose the posterior into a likelihood step and a prior step: Langevin dynamics handles the likelihood step, while the Stochastic Interpolants (SI) framework integrates a pretrained flow matching model into the prior step via a reverse-time SDE. The paper also shows connections to prior plug-and-play (PnP) methods. Thanks to the straight probability paths of flow priors and a novel time-step correction technique for the reverse SDE, FlowSGS requires fewer network evaluations per prior step than PnP diffusion samplers. Experiments across a range of inverse problems achieve state-of-the-art performance, including, for the first time for a flow-based solver, experiments on a nonlinear inverse problem (Fourier phase retrieval).
Paper Overview
Field: Computer Vision
Authors: Tianao Li, Xinhui Qian, Emma Alexander
Published: 2026-09-17
arXiv: 2609.20769
Abstract
Flow matching has emerged as the state-of-the-art generative model and has been used for plug-and-play (PnP) priors to solve inverse problems in computational imaging. However, existing flow-based inverse solvers assume linear forward models and/or make simplifying approximations in posterior sampling. To circumvent these problems, the authors introduce FlowSGS, a flow-based posterior sampling method using Split Gibbs Sampling (SGS) to decompose the posterior into a likelihood step and a prior step.
Key contributions:
- Likelihood step: sampled using Langevin dynamics.
- Prior step: integrates a pretrained flow model via the Stochastic Interpolants (SI) framework, using SI's reverse-time SDE; connections to previous PnP methods are shown.
- Efficiency: thanks to the straight probability paths of flow priors and a novel time-step correction technique for the reverse SDE, FlowSGS requires fewer network evaluations in the prior step than PnP diffusion samplers.
- Results: state-of-the-art performance across a range of inverse problems, including the first experiments on a nonlinear inverse problem (Fourier phase retrieval) for a flow-based inverse solver.
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*Auto-collected on 2026-09-19*
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